An antenna is a device that transmits or receives electromagnetic waves. It acts as a transition between guided and free space electromagnetic wave propagation. Common types of antennas include wire antennas like dipoles and loops, aperture antennas like parabolic dishes and horns, and antenna arrays. Key antenna parameters that are described include radiation patterns, beam area and efficiency, directivity, gain, and radiation resistance. Common topics like polarization, reflection and refraction, guided wave propagation, launching electromagnetic waves, and reciprocity are also covered at a high level.

1. Introduction to antennas
Michel Anciaux / APEX
November 2004

2. What is an antenna?
• Region of transition between guided and free space propagation
• Concentrates incoming wave onto a sensor (receiving case)
• Launches waves from a guiding structure into space or air
(transmitting case)
• Often part of a signal transmitting system over some distance
• Not limited to electromagnetic waves (e.g. acoustic waves)

3. Free space electromagnetic wave
Magnetic
field
Electric
field
Direction of
propagation
Magnetic
Field [A/m]
Electric
Field [V/m]
Time [s]
Time [s]
•Disturbance of EM field
•Velocity of light (~300 000 000 m/s)
•E and H fields are orthogonal
•E and H fields are in phase
•Impedance, Z0: 377 ohms
x
y z

4. EM wave in free space
)
(
0
z
t
j
x e
E
E 
 

2
2
0
0
2
2
1
z
E
t
E x
x







2
2
0
0
2
2
1
z
H
t
H y
y







)
(
0
z
t
j
y e
H
H 
 



2

f



2

f
0
0
1


 
wavelength
Phase constant
frequency
0
0
0



Z
0
0
0
H
E
Z 
Magnetic
field
Electric
field
Direction of
propagation
x
y z

5. Wave in lossy medium
t
j
z
j
z
t
j
z
x e
e
e
E
e
e
E
E 








 


0
0


 j


Attenuation constant
Phase constant


Propagation constant
Attenuation
increases with z
Phase varies
with z
Periodic time
variation

6. Power flow
H
E
S





0
2
0
2
2
1
1
2
1
Z
H
Z
E
S y
x
av 

Poynting vector
Average power density

7. Polarisation of EM wave
Electrical field, E
vertical
horizontal
circular

8. Reflection, refraction
i
r 
 
)
sin(
)
sin(
2
1
i
t 


 
)
sin(
)
sin( 2
2
1
1
i
t 
 




Reflection
Refraction
if both media are lossless
i
r
E
E


Reflection coefficient: Depends on media, polarisation
of incident wave and angle of incidence.
Reflection and refraction affect polarisation

9. Guided electromagnetic wave
• Cables
– Used at frequencies below 35 GHz
• Waveguides
– Used between 0.4 GHz to 350 GHz
• Quasi-optical system
– Used above 30 GHz

10. Guided electromagnetic wave (2)
• TEM wave in cables and quasi-optical systems (same as free space)
• TH,TE and combinations in waveguides
– E or H field component in the direction of propagation
– Wave bounces on the inner walls of the guide
– Lower and upper frequency limits
– Cross section dimensions proportional to wavelength

11. Rectangular waveguide

12. Launching of EM wave
Open up the cable and
separate wires
Dipole antenna
Open and flare up
wave guide
Horn
antenna

13. Transition from guided wave to free space wave

14. Reciprocity
• Transmission and reception antennas can be used interchangeably
• Medium must be linear, passive and isotropic
• Caveat: Antennas are usually optimised for reception or transmission
not both !

15. Basic antenna parameters
• Radiation pattern
• Beam area and beam efficiency
• Effective aperture and aperture efficiency
• Directivity and gain
• Radiation resistance

16. Radiation pattern
•Far field patterns
•Field intensity decreases with increasing distance, as 1/r
•Radiated power density decreases as 1/r2
•Pattern (shape) independent on distance
•Usually shown only in principal planes

2
D
2
r
:
field
Far  D : largest dimension of the antenna
e.g. r > 220 km for APEX at 1.3 mm !

17. Radiation pattern (2)
)
,
( 


E )
,
( 


E
2
0
2
2
)
,
(
)
,
(
)
,
( r
Z
E
E
P





 
 

Field patterns
max
)
,
(
)
,
(
)
,
(






P
P
Pn 
+ phase patterns
)
,
( 

 )
,
( 


HPBW: half power beam width

18. Beam area and beam efficiency

  





 







4
2
0 0
)
,
(
)
sin(
)
,
( d
P
d
d
P n
n
A
Main beam area
Minor lobes area


  d
P
beam
Main
n
M )
,
( 



  d
P
lobes
or
n
m
min
)
,
( 

m
M
A 




Beam area
A
M
M




Main beam efficiency

19. Effective aperture and aperture efficiency
Receiving antenna extracts power from incident wave
e
in
rec A
S
P 

For some antennas, there is a clear physical aperture
and an aperture efficiency can be defined
p
e
ap
A
A


A
e
A


2

Aperture and beam area are linked:

20. Directivity and gain
average
P
P
D
)
,
(
)
,
( max





A
n d
P
D










4
)
,
(
4
4
Isotropic antenna: 
4

A 1

D
2
4

 e
A
D 
From pattern
From aperture
only
losses
ohmic
to
due
lower than
is
)
1
(0
factor
efficiency
Gain
D
G
k
k
D
k
G
g
g
g




Directivity

21. Radiation resistance
• Antenna presents an impedance at its terminals
A
A
A jX
R
Z 

•Resistive part is radiation resistance plus loss resistance
L
R
A R
R
R 

The radiation resistance does not correspond to a real resistor
present in the antenna but to the resistance of space coupled
via the beam to the antenna terminals.

22. Types of Antenna
• Wire
• Aperture
• Arrays

23. Wire antenna
• Dipole
• Loop
• Folded dipoles
• Helical antenna
• Yagi (array of dipoles)
• Corner reflector
• Many more types
Horizontal dipole

24. Wire antenna - resonance
• Many wire antennas (but not all) are used at or near resonance
• Some times it is not practical to built the whole resonant length
• The physical length can be shortened using loading techniques
– Inductive load: e.g. center, base or top coil (usually adjustable)
– Capacitive load: e.g. capacitance “hats” (flat top at one or both ends)

25. Yagi-Uda
Elements Gain
dBi
Gain
dBd
3 7.5 5.5
4 8.5 6.5
5 10 8
6 11.5 9.5
7 12.5 10.5
8 13.5 11.5

26. Aperture antenna
• Collect power over a well defined aperture
• Large compared to wavelength
• Various types:
– Reflector antenna
– Horn antenna
– Lens

27. Reflector antenna
• Shaped reflector: parabolic dish, cylindrical antenna …
– Reflector acts as a large collecting area and concentrates power onto
a focal region where the feed is located
• Combined optical systems: Cassegrain, Nasmyth …
– Two (Cassegrain) or three (Nasmyth) mirrors are used to bring the focus
to a location where the feed including the transmitter/receiver can be
installed more easily.

28. Cassegrain antenna
• Less prone to back scatter than simple parabolic antenna
• Greater beam steering possibility: secondary mirror motion
amplified by optical system
• Much more compact for a given f/D ratio

29. Cassegrain antenna (2)
• Gain depends on diameter, wavelength, illumination
• Effective aperture is limited by surface accuracy, blockage
• Scale plate depends on equivalent focal length
• Loss in aperture efficiency due to:
– Tapered illumination
– Spillover (illumination does not stop at the edge of the dish)
– Blockage of secondary mirror, support legs
– Surface irregularities (effect depends on wavelength)
deviation
surface
of
rms
4
cos
2







 



g
K
96
.
0
:
efficiency
blockage
94
.
0
:
efficiency
spillover
87
.
0
:
efficiency
taper
b
s
t






At the SEST:

30. Horn antenna
• Rectangular or circular waveguide flared up
• Spherical wave fronts from phase centre
• Flare angle and aperture determine gain

31. Short dipole
)
1
1
(
2
)
cos(
3
2
0
)
(
0
r
j
cr
le
I
E
r
t
j
r








)
1
1
(
4
)
sin(
3
2
2
0
)
(
0
r
j
cr
r
c
j
le
I
E
r
t
j






 



)
1
(
4
)
sin(
2
)
(
0
r
cr
j
le
I
H
r
t
j









2
r
1
as
varies
P
r
1
as
vary
H
E
,
2




and
r
for 
•Length much shorter than wavelength
•Current constant along the length
•Near dipole power is mostly reactive
•As r increases Er vanishes, E and H gradually become in phase


 


l
r
e
I
j
E
r
t
j
)
sin(
60 )
(
0



32. Short dipole pattern
Short dipole power pattern
X Y
 Z

( )
.
0
30
60
90
120
150
180
210
240
270
300
330
0.8
0.6
0.4
0.2
0
PN

.
Short dipole power pattern
X Y
 Z

( )
.
3
8

A
5
.
1

D
2
2
80 








l
Rr

33. Thin wire antenna
•Wire diameter is small compared to wavelength
•Current distribution along the wire is no longer constant
dipole
fed
-
centre
2
2
sin
)
(
e.g. 0 














 y
L
I
y
I


•Using field equation for short dipole,
replace the constant current with actual distribution
 
 
point
feed
at
current
I
dipole,
fed
-
centre
sin
2
cos
2
cos
cos
60
0
)
(
0



































L
L
r
e
I
j
E
r
t
j

34. Thin wire pattern
thin wire centre fed dipole power pattern
X Y
 Z

( )
l 1

2

 A 7.735
 D 1.625

thin wire centre fed dipole power pattern
X Y
 Z

( )
l 1.395

 A 5.097
 D 2.466

thin wire centre fed dipole power pattern
X Y
 Z

( )
l 10

 A 1.958
 D 6.417


35. 0
30
60
90
120
150
180
210
240
270
300
330
Power pattern of 2 isotropic sources
Pn

d 1

2
  0deg

0
30
60
90
120
150
180
210
240
270
300
330
Power pattern of 2 isotropic sources
Pn

d 1

2
  90
 deg

0
30
60
90
120
150
180
210
240
270
300
330
1.5
1
0.5
0
Field Pattern of 2 isotropic sources
E i
 
i
0
30
60
90
120
150
180
210
240
270
300
330
Power pattern of 2 isotropic sources
Pn

d 1

2
  45
 deg

0
30
60
90
120
150
180
210
240
270
300
330
1.5
1
0.5
0
Field Pattern of 2 isotropic sources
E i
 
i
0
30
60
90
120
150
180
210
240
270
300
330
Power pattern of 2 isotropic sources
Pn

d 1

2
  135
 deg

Array of isotropic point sources – beam shaping

x
y
d

36. Array of isotropic point sources – centre-fed array
0
30
60
90
120
150
180
210
240
270
300
330
0.8
0.6
0.4
0.2
0
Field Pattern of n isotropic sources
Efi
i
n 8
  0deg
 d 0.5

0
30
60
90
120
150
180
210
240
270
300
330
0.8
0.6
0.4
0.2
0
Field Pattern of n isotropic sources
Efi
i
n 3
  67.5
 deg
 d 0.5






 
 )
cos(
2
)
(
d
 
2
/
sin
2
sin
1
)
(










n
n
En

x
y
d
 
 
0

37. Array of isotropic point sources – end-fired
0
30
60
90
120
150
180
210
240
270
300
330
0.8
0.6
0.4
0.2
0
Field End-fired, n isotropic sources
Efi
i
n 10
  108
 deg
 d 1

4

end-fired array,n elements power pattern
X Y
 Z

( )
n 10
 d 0.25

 A 0.713
 D 17.627

 
 
n
d 




 

 1
cos
2
)
(



















2
sin
2
sin
2
sin
)
(




n
n
En

x
y
d

 

0

38. Pattern multiplication
The total field pattern of an array of non-isotropic but similar point sources
is the product of the individual source pattern and the pattern of an array of
isotropic point sources having the same locations,relative amplitudes and
phases as the non-isotropic point sources.
0
30
60
90
120
150
180
210
240
270
300
330
0.8
0.6
0.4
0.2
0
Primary field pattern
Ef1i
i
n 2
 1 104
 deg
 d1 0.3

0
30
60
90
120
150
180
210
240
270
300
330
0.8
0.6
0.4
0.2
0
Secondary field pattern
Ef2i
i
n 2
 2 180deg
 d2 0.6

0
30
60
90
120
150
180
210
240
270
300
330
0.8
0.6
0.4
0.2
0
Total field pattern
Efi
i
Total pattern of two primary sources
(each an array of two isotropic sources)
replacing two isotropic sources (4
sources in total).

39. Patterns from line and area distributions
•When the number of discrete elements in an array becomes large,
it may be easier to consider the line or the aperture distribution as
continuous.
• line source:
line
to
normal
anglefrom
length,
l
,
)
sin(
u
)
(
2
)
(
1
1



 





l
dx
e
x
f
l
u
E jux
•2-D aperture source:
       
 
on
distributi
field
aperture
)
,
(
)
,
(
, sin
cos
sin

 

y
x
f
dy
dx
e
y
x
f
E
aperture
y
x
j 






40. Fourier transform of aperture illumination
Diffraction limit
only
estimate
rough
D
HPBW


10 5 0 5 10
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Ep
xp
300 240 180 120 60 0 60 120 180 240 300
50
45
40
35
30
25
20
15
10
5
0
Far field
angular distance [arcsec]
Power
pattern
[dB]
3

10 5 0 5 10
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Ep
xp
300 240 180 120 60 0 60 120 180 240 300
50
45
40
35
30
25
20
15
10
5
0
Far field
angular distance [arcsec]
Power
pattern
[dB]
3


41. Predicted power pattern - SEST 1.3 mm- off axis 130 mm
EFN
.
Far field pattern from FFT of Aperture field distribution
Predicted power pattern - flat illumination
EFN
.
Predicted power pattern - SEST 1.3 mm- on axis
EFN
.

42. Effect of edge taper
Predicted power pattern -16dB taper
EFN
.
Predicted power pattern -8dB taper
EFN
.

43. dBi versus dBd
•dBi indicates gain vs. isotropic antenna
•Isotropic antenna radiates equally well in all directions,
spherical pattern
•dBd indicates gain vs. reference half-wavelength dipole
•Dipole has a doughnut shaped pattern with a gain of 2.15 dBi
dB
dBd
dBi 15
.
2



44. Feed and line matching
•The antenna impedance must be matched by the line feeding
it if maximum power transfer is to be achieved
•The line impedance should then be the complex conjugate of
that of the antenna
•Most feed line are essentially resistive

45. Signal transmission, radar echo
,
,
, 
t
t
et G
P
A
• Receiving antenna
• Transmitting antenna
r
r
er G
P
A ,
,
t
r
t
r
t
t
r P
G
G
r
G
r
P
G
P
2
2
2
4
4
4















 







 4
3
2
2
2
2
4
4
4
4 r
G
G
P
G
r
r
P
G
P r
t
t
r
t
t
r 



Radar return
S, power density Effective receiving area
S, power density Effective receiving area
Reflected
power density
(area)
section
cross
radar



46. Antenna temperature
• Power received from antenna as from a black body or the radiation
resitance at temperature Ta

47. The end